发表机构
New York University Shanghai; NYU-ECNU Institute of Mathematical Sciences, New York University Shanghai（纽约大学上海分校; 纽约大学上海分校 纽约大学-华东师范大学数学科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出有限状态连续时间马尔可夫链神经元框架，可统一逼近多种激活函数，实现激活灵活的ANN到SNN转换，并证明逼近误差界，实验显示裁剪可优化成本-精度权衡。
AI 中文摘要
大多数ANN到SNN转换方法依赖于源激活函数与脉冲神经元动力学之间的特定对应关系。我们提出了一种有限状态连续时间马尔可夫链（CTMC）神经元框架，其稳态脉冲通量可以近似紧致区间上的任意连续非负单调激活函数。对于具有仿射输入依赖转移的广义CTMC族，我们证明了在该函数类上以任意精度进行均匀逼近，并推导出显式的逼近误差界。在实践中，两状态和三状态CTMC在评估的输入范围内拟合ReLU、sigmoid、softplus和裁剪ReLU，并针对每种激活函数评估了相应的MLP转换，采用逐层速率缩放。适度的裁剪改善了MNIST MLP上的转换成本-精度权衡，并在匹配的ANN-SNN精度差距标准下，将VGG-11/MNIST的SynOps减少了27%，而在VGG-11/CIFAR-10上趋势则相反。平均场和逐层诊断表明，有限窗口采样和终端层不匹配是主要的残余误差。总体而言，我们的结果确立了有限状态CTMC神经元作为激活灵活ANN到SNN转换的理论基础框架，超越了固定的激活-神经元对应关系。
英文摘要
Most ANN-to-SNN conversion methods rely on a specific correspondence between the source activation and the spiking neuron dynamics. We propose a finite-state continuous-time Markov chain (CTMC) neuron framework whose stationary spike flux can approximate every continuous nonnegative monotone activation function on a compact interval. For a generalized CTMC family with affine input-dependent transitions, we prove uniform approximation to arbitrary accuracy over this function class and derive an explicit approximation error bound. In practice, two- and three-state CTMCs fit ReLU, sigmoid, softplus, and clipped ReLU on the evaluated input ranges, and we evaluate corresponding MLP conversions for each activation with layerwise rate scaling. Moderate clipping improves the conversion cost-accuracy tradeoff on the MNIST MLP and reduces SynOps by 27% on VGG-11/MNIST at matched ANN-SNN accuracy gap criteria, whereas the trend reverses on VGG-11/CIFAR-10. Mean-field and layerwise diagnostics indicate that finite-window sampling and terminal-layer mismatch are the main residual errors. Overall, our results establish finite-state CTMC neurons as a theoretically grounded framework for activation-flexible ANN-to-SNN conversion beyond fixed activation-neuron correspondences.
